Datasets used in the paper entitled "", containing the following acquisitions: 1) Simulated abdomen data set: we have synthetized a 3D volume using the simulation environment XCAT based on the extended cardio-torso phantom. We simulated a T1-weighted acquisition using the following acquisition parameters: TE/TR=1.5/3ms, flip angle=60º, acquisition matrix size=60x60x32. A 32-coil acquisition was simulated by modulating the image using artificial sensitivity maps coded for each coil. The noise-free coil images were transformed into the \bk--space and corrupted with synthetic Gaussian noise characterized by the matrices \(\Gamma_k\)and \(C_k\) with SNR=25 for each coil, and the correlation coefficient between coils was set to \(\rho\)=0.1$. For statistical purposes, 4000 realizations of each image were used. 2) Water phantom acquisition: A MR phantom sphere with solution (GE Medical Systems, Milwaukee, WI) was scanned in a 32-channel head coil on a 3.0T scanner (MR750, GE Healthcare, Waukesha, WI). A spoiled gradient-echo acquisition with 100 realizations of the same fully-encoded k-space sampling was used. Acquisition parameters included: coronal view, TE/TR=0.96/3.69ms, flip angle=12º, field of view=22x22$x30.7\(cm³\), acquisition matrix size=60x60x32, bandwidth=62.5KHz. We corrected for \(B_0\) field drift related phase variations and magnitude decay by a pre-processing step. First we estimated the phase-shift between realizations from the center of the k-space as a cubic function of time and removed it afterwards. And, second, we estimated the magnitude-decay in the k-space as a linear function and substracted it in order not to affect the noise. 3) In vivo acquisition: in order to assess the feasibility of the proposed method, after obtaining the approval fo the local institutional review board (IRB), a volunteer was scanned in a 32-channel head coil on a 3.0T scanner (MR750, GE Healthcare, Waukesha, WI). A spoiled gradient-echo acquisition of a fully-encoded \bk--space sampling was used. Acquisition parameters included: coronal view, TE/TR=2.2/5.7ms, flip angle=12º,field of view=22x22x22\(cm³\), matrix size=220x220x220, bandwidth=62.5$KHz.

The authors acknowledge MICIN for grants TEC2013-44194P, TEC 2014-57428 and TEC2017-82408-R, as well as Junta de Castilla y León for grant VA069U16. The first author acknowledges MINECO for FPI grant BES-2014-069524.